Problem Set 2

Assigned: Feb. 5:
Due: Feb. 19

Programming and experimental assignment

Programming

Implement the GSAT algorithm for the N-queens
problem using the following three states spaces.

State space 1.

A state is any placement of queens on the board.
An operator is either to add or to delete a queen. The error function
is (the number of pairs that attack one another) + max(0,N-(the number of
queens on the board)

State space 2

A state is any placement of 1 queen per column. An operation is to change
the column of 1 queen. The error function is the number of pairs of
queens that attack one another.

For example, for the 8-queens, one state would be [4,5,1,3,3,1,8,6]
The error function would be 9: 1,4 attacks 2,5; 2,5 attacks 4,3; 2,5
attacks 6,1; 3,1 attacks 5,3; 3,1 attacks 6,1; 3,1 attacks 8,6;
4,3 attacks 5,3; 4,3 attacks 6,1; 5.3 attacks 8,6.
One operator would be to move
the queen in the 3rd column to 7, giving [4,5,7,3,3,1,8,6].

State space 3

A state is a placement of 1 queen per column and row; that is, a
permutation of the columns into the rows. An operator would be to
swap the row value for two columns. The error function is the number
of pairs of queens that attack one another.

For example one state would be [4,6,8,1,3,5,7,2]. An operator would
be to switch columns 4 and 8, giving [4,6,8,2,3,5,7,1].

Parameters:

Use an upper bound of 2000 for the inner loop of GSAT and
an upper bound of 5 for the outer loop. Extra credit: Find a good
tuning for these parameters as a function of the size of the various
problems.

Coding

You may use any language you like, as long as it runs on the Sun system.

Experiment

Test each of the above state space searches with N=25, 50, 75, 100.
Run twenty instances of each. For each state space and for each size, report:

For each size, the percentage that find a solution.

The mean, the maximum, the minimum,
and the standard deviation of the running times, in terms of total
number of iterations of the internal loop, over the set of runs that
find a solution.

You do not have to let
any instance of an experiment run for more than 1 minute.

Submitting the assignment

Sean McLaughlin (seanmcl@cs.nyu.edu) is the TA for this course. You
should mail him

The source code for your program or programs

A readme file saying how to run your program(s).

A report on the experimental results

Email the report to me (davise@cs.nyu.edu) as well.

If you prefer, you may hand in the report in hard copy.

Late Assignments

Since I am not handing out solutions, I can be more flexible about
accepting late assignments. There will be a late penalty of 0.5 out
of 10 for each week late. (Round up to get the number of weeks late;
e.g. an assignment handed in day after class is considered 1 week late.)